English

Estimates of size of cycle in a predator-prey system II

Dynamical Systems 2023-11-29 v1

Abstract

We prove estimates for the maximal and minimal predator and prey populations on the unique limit cycle in a standard predator-prey system. Our estimates are valid when the cycle exhibits small predator and prey abundances and large amplitudes. The proofs consist of constructions of several Lyapunov-type functions and derivation of a large number of non-trivial estimates, and should be of independent interest. This study generalizes results proved by the authors in (Differ Equ Dyn Syst 30, 131-159 (2022)) to a wider class of systems and, in addition, it gives simpler proofs of some already known estimates.

Keywords

Cite

@article{arxiv.2311.16735,
  title  = {Estimates of size of cycle in a predator-prey system II},
  author = {Niklas L. P. Lundström and Gunnar J. Söderbacka},
  journal= {arXiv preprint arXiv:2311.16735},
  year   = {2023}
}